Math

If x=1 is the vertical asymptote and y=-3 is the horizontal asymptote for the graph of the function f
which of the following could be the equation of the curve
A.f(x)=(-3x^2)/(x-1)
B.f(x)=-3(x-1)/(x+3)
C.f(x)=-3(x^2-1)/(x-1)
D.f(x)=-3(x^2-1)/(x-1)^2

  1. 👍
  2. 👎
  3. 👁
  1. The answer is D but can someone explain to me why it is?

    1. 👍
    2. 👎
  2. x=1 is the vertical asymptote
    so you need a fraction with (x-1) in the denominator
    since division by zero is undefined, and if the numerator is not zero, there will be a vertical asymptote there.

    and y=-3 is the horizontal asymptote
    Since there is a horizontal asymptote, the degree of the numerator is equal to that of the denominator.
    Since the asymptote is at y = -3, the ratio of the leading coefficients is -3.
    So, an easy function would be 3(x-k)/(x-1) where k≠1
    That is not one of the choices, but D is the only choice which has the required factors.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra

    Describe the vertical asymptote and hole for the graph of (x^2+x-6)/(x^2-9). a. asymptote: x=2; hole: x=-3 b. asymptote: x=3; hole: x=2 c. asymptote: x=-3; hole: x=3 d. asymptote: x=3; hole: x=-3 I know that it has to either be b

  2. Precalculus

    Write an equation for rational function with given properties. a) a hole at x = 1 b) a vertical asymptote anywhere and a horizontal asymptote along the x-axis c) a hole at x = -2 and a vertical asymptote at x = 1 d) a vertical

  3. Math

    Give an example of a rational function that has vertical asymptote x = 3 and x = -3, horizontal asymptote y = 2 and y-intercept is (0, 4)

  4. Calculus AB

    Let f be the function that is given by f(x)=(ax+b)/(x^2 - c). It has the following properties: 1) The graph of f is symmetrical with respect to the y-axis 2) The graph of f has a vertical asymptote at x=2 3) The graph of f passes

  1. Algebra

    Enter the equations of the asymptotes for the function f(x) . f(x)= −(2/x+4) − 6 Vertical Asymptote: ? Horizontal Asymptote: ?

  2. Rational Functions

    Write an equation for a rational function whose graph has the following properties: x-intercept of 3 y-intercept of -3 vertical asymptote of x=-2 horizontal asymptote of y=2

  3. Algebra

    write an equation for a rational function that has a vertical asymptote of -4, a horizontal asymptote of 3, and vertically shrinks the graph by a factor of 5 (compared to the graph of y=1/x). So far I have Y=3x/x+4 but I can't

  4. Calculus

    If the graph of y = (ax - b)/(x - c) has a horizontal asymptote y=5 and a vertical asymptote x = − 2 , then b cannot be equal to what?

  1. Math

    State an equation of a rational function that satisfies the given conditions: vertical asymptote at x=5, horizontal asymptote at y=-3, and x-intercept is 5/2. Need help solving.

  2. Math

    f(x) = tan x / sin x Find the vertical asymptote. Describe its behavior to the left and right of the vertical asymptote.

  3. Gr.11 - Rational functions graphing.

    1. Identify a rational function whose graph is a horizontal line except for two holes. Graph the function. 2. Identify a rational function who graph lies entirely above the x-axis and has a single vertical asymptote. Graph the

  4. math

    There is a vertical asymptote at x=2, and a horizontal asymptote at y=3. Construct a suitable rational function f(x).

You can view more similar questions or ask a new question.